VSdecomp (version 0.1.1)

linear_projection: Linear Projection

Description

estimates the linear model \(y = \beta*X + \epsilon\) and returns its linear components, grouped according to X.list.

Usage

linear_projection(
  y,
  X.list,
  data,
  wgt = rep(1, nrow(data)),
  year = rep(1, nrow(data)),
  comp.names = NULL
)

Arguments

y

a character specifying the name of the outcome variable (e.g. "wage"). Note that this variable is standardized before it's projected onto X.

X.list

a list containing the names of all the variables needed for the linear projection, grouped according to the components will later be used in the skewness decomposition. For example: for X.list = list("x1", c("x2", "x3")) the following components are returned: \(\beta1X1\), (\(\beta2X2+ \beta3X3\)), \(\epsilon\). Currently interactions aren't supported, so the user should insert them manually.

data

a data frame with all the variables specified in X.list and y.

wgt

an optional vector of weights.

year

an optional vector of years. if provided, the projection is done for each year separately.

comp.names

an optional vector specifying name for each component.

Value

a matrix with the (centered) components specified by X.list + residuals. Note that each row is summed (up to a constant) to the standardized version of y, and each column to 0 (both by year).

Examples

# NOT RUN {
#gen data
n <- 1000
X <- matrix(rnorm(n*3), ncol = 3)
colnames(X) <- c("x1", "x2", "x3")
beta <- c(1,2,3)
wage <- X %*% beta + rnorm(n)
dat <- as.data.frame(cbind(wage, X))
colnames(dat)[1] <- "wage"
res <- linear_projection("wage", X.list = list("x1", c("x2", "x3")), data = dat)
#each row is summed (up to a constant) to the standardized wage:
stand_wage <- (wage - mean(wage)) / sd(wage)
diff <- apply(res, 1, sum) - stand_wage
summary(diff)
# }